WASHINGTON (AP) — Majority Democrats in the Senate won approval Tuesday for one of President Barack Obama’s key judicial nominees, the first of his picks to win confirmation since they weakened the chamber’s filibuster rules.

Senators voted 56-38 to approve Washington lawyer Patricia Millett to join the US Court of Appeals for the District of Columbia, the nation’s second most powerful court.

Both sides saw Millett’s appointment as pivotal. It will give Democratic-appointed judges a 5-4 majority over those chosen by Republican presidents for that court, which rules on the legality of White House actions and federal agency regulations.

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In Tuesday’s vote, Sens. Susan Collins of Maine and Lisa Murkowski of Alaska were the only Republicans to join Democrats in supporting Millett.

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Republicans say Watt is unqualified to lead that agency, which oversees the taxpayer-owned mammoth home mortgage home lenders Freddie Mac and Fannie Mae. Democrats say Watt, a 21-year House veteran, has the necessary skills and is opposed by Republicans because they think he is too liberal.

Millett, the first nominee to emerge from the highly partisan filibuster fight, is a veteran who has argued 32 cases at the Supreme Court and has strong bipartisan credentials.

A Harvard Law School graduate, Millett served as an assistant to the solicitor general under President Bill Clinton, a Democrat, and President George W. Bush, a Republican. She then joined the Supreme Court practice at Akin Gump, one of Washington’s biggest law firms.

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Over the next two weeks, Democratic leaders also plan to win final Senate approval for two other Obama nominees to the D.C. Circuit, as well as his picks to head the Federal Reserve and the Department of Homeland Security.

Monday’s votes were coming the morning after Republicans responded to changes Democrats made to Senate filibuster traditions by slowing down 76 mostly minor nominations.

The move by Senate Republicans won’t stop any of the nominations — Democrats can now approve them by a simple majority. But it showed Republicans would make Democrats pay a price for their decision to change filibuster practices and showed that tensions over nominations are still roiling the Senate.

Last month, Democrats used their effective 55-45 majority to upend decades of Senate filibuster traditions and allow simple majority votes on most presidential appointments, excluding Supreme Court nominees. Before the change, the president’s party needed 60 votes to prevent opposing senators from blocking a nominee.

Republicans responded furiously as they left for the Senate’s Thanksgiving break and continued to rail against the changes on Monday.

Reid said Alexander’s objections were ‘‘as flat as a bottle of beer that’s been open for six months.’’ He then scheduled votes on several nominations.

Most of the nominees slowed by Alexander’s objection were for minor posts, including some federal judges, lower-level ambassadors and government boards.

Reid planned to move ahead with votes on six key Obama nominees before the Senate adjourns next week — Millett and fellow D.C. appeals court nominees Cornelia ‘‘Nina’’ Pillard and Robert Wilkins; Yellen and Johnson; and Watt.

Republicans retain options under Senate rules to slow but not stop presidential appointments by themselves. For appeals court and Cabinet-level appointments they can still make majority Democrats put off a final confirmation vote for up to 30 hours. For lesser posts like Watt's, the maximum is eight hours.

Republicans can also force at least one procedural vote on each nominee before roll calls are taken to end filibusters and for final approval. Each requires only a simple majority for Democrats to prevail.

Republicans have little criticism of Millett and Obama’s other D.C. Circuit nominees. Instead, they've said they oppose adding judges to the court and tilting its balance when its caseload is smaller than other federal appeals courts.